Wave Propagation in Orthogonally Supported Periodic Curved Panels

Pany, Chitaranjan; Parthan, S.; Mukhopadhyay, Madhujit

doi:10.1061/(asce)0733-9399(2003)129:3(342)

Cited by 6 publications

(13 citation statements)

References 15 publications

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“…Using the FE method, a periodic unit can be represented by a model with the internal and boundary degrees of freedom (Pany et al, 2003). Each periodic unit is joined to its adjacent units at all sides and corners.…”

Section: Stiffness and Mass Matrix Of A Single Curved Panel By Finite...mentioning

confidence: 99%

“…The basic method of computing the free wave motion in any one-dimensional or quasi-one dimensional continuous periodic systems has been applied to uniform cylindrical shells. Free wave propagation has been studied in the unsupported shell (Pany et al, 1999;, axial line simple support infinitely curved panels (Pany and Parthan, 2003a), and orthogonal line simple support curved panels (Pany et al, 2003) using the periodic structure theory with FEM (PS-FEM). In the case of a circular cylindrical shell, each periodic element is a segment of the shell between two consecutive nodal positions.…”

Section: Introductionmentioning

confidence: 99%

“…Earlier, the FE method in wave propagation analysis using the periodic structure (PS) theory has been applied to multispan curved panel rests on orthogonal array of the equi-spaced simple line support by Pany et al (2003) to determine the propagation surface of circular cylindrical shells. In this method, the basic periodic unit (i.e., any of the repeating units of curved panel) is modeled by using the arbitrary triangular shallow shell FEM of Cowper et al (1970) and Sinha et al (1992).…”

Section: Introductionmentioning

confidence: 99%

“…Albeit these phenomena are well comprehended, most literature reports on the periodic engineering structures are dedicated to the development of theoretical and numerical approaches to know its wave propagation behavior and characteristics. The purpose of this work was to extend the approach (Abdel-Rahman and Petyt, 1980; Pany et al, 2003) to analyze the wave propagation characteristics (propagation surfaces) in 2D periodic (orthogonal line supported) plate structures. Here, the shallow shell FE is employed to model a periodic plate unit considering infinite radius of curvature.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An Insight on the Estimation of Wave Propagation Constants in an Orthogonal Grid of a Simple Line-Supported Periodic Plate Using a Finite Element Mathematical Model

Pany

2022

Front. Mech. Eng.

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This article describes the propagation of free waves in a two-dimensional periodic plate using the finite element (FE) method. The advantage of periodic structure analysis is that all the dynamic properties of a finite structure are derived from a single phase-frequency curve or surface. Infinite plates are considered as a combination of periodic plates on an orthogonal array of simple, evenly spaced line supports. A single periodic unit of the system is represented by a more accurate high-precision arbitrary triangular shallow shell FE model to find the plane wave frequency in terms of the propagation constants of the 2D periodic plate. Only the purely propagating waves with no attenuation are considered here. The natural frequency of the infinite plate was obtained for different propagation constants in the two directions of the plate. The results are compared with the literature data. The bounding frequency of the propagation surface is compared to the data published from single square and rectangular plates with different edge boundary conditions. In addition, the natural frequency of the plate supported by finite line support with spans Nx (x-direction) and Ny (y-direction) is compared with the frequency obtained from the propagation curve by the discretization principle. The comparison is seen to be very close. It is found that the current PS-FEM approach can be used to generate dispersion relations with reasonable accuracy.

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Section: Stiffness and Mass Matrix Of A Single Curved Panel By Finite...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An Insight on the Estimation of Wave Propagation Constants in an Orthogonal Grid of a Simple Line-Supported Periodic Plate Using a Finite Element Mathematical Model

Pany

2022

Front. Mech. Eng.

Self Cite

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“…Finite element methods (FEMs) have become a popular tool for the dynamic analyses of complex structures. Various forms of elements such as shell element combined with beam element (Hota and Chakravorty, 2007), axisymmetric elements (Al-Najafi and Warburton, 1970; Raj et al., 1995), hierarchical finite elements (Bardell and Mead, 1989a,b), super shell elements (Mustafa and Ali, 1987a; Jiang and Olson, 1994), stiffened elements (Sinha and Mukhopadhyay, 1994; Samanta and Mukhopadhyay, 2004), semi-loof and facet shell elements (Mustafa and Ali, 1987b), isoparametric elements (Palani et al., 1992; Nayak and Bandyopadhyay, 2002a,b), semi-analytical finite elements (Stanley and Ganesan, 1997) and curved triangular shell elements (Pany, 2003) have been used to capture the vibratory characteristics of stiffened shells or panels. A spectral finite element model of the periodically stiffened shell was developed by Solaroli et al.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of doubly curved shallow shells reinforced by any number of beams with arbitrary lengths

Jiang

Yang

et al. 2014

Journal of Vibration and Control

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This study focuses on the free linear vibrations of doubly curved shallow shells reinforced by any number of beams of arbitrary lengths. Distributed elastic restraints are used to specify generally the boundary conditions along the shell edges and the coupling conditions between the shell and its reinforcing beams. Both the shell and stiffening beams are considered as independent structural components carrying three-dimensional displacement fields. Each of the displacements is invariably expressed as a simple trigonometric series with accelerated and uniform convergence over the solution domains of interest. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh-Ritz technique. As illustrated by examples, the current method provides a unified means for solving a wide range of shell problems involving various practical complications with respect to, for example, the boundary conditions, the coupling conditions, the number of stiffeners, and the lengths and locations of the stiffeners.

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Exploring Black Holes: From Hawking Radiation to Quantum Hair-Insights and Challenges in Modern Astrophysics

Kanu,

Gupta,

Gupta

2024

J. Inst. Eng. India Ser. C

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Wave Propagation in Orthogonally Supported Periodic Curved Panels

Cited by 6 publications

References 15 publications

An Insight on the Estimation of Wave Propagation Constants in an Orthogonal Grid of a Simple Line-Supported Periodic Plate Using a Finite Element Mathematical Model

An Insight on the Estimation of Wave Propagation Constants in an Orthogonal Grid of a Simple Line-Supported Periodic Plate Using a Finite Element Mathematical Model

Free vibration analysis of doubly curved shallow shells reinforced by any number of beams with arbitrary lengths

Exploring Black Holes: From Hawking Radiation to Quantum Hair-Insights and Challenges in Modern Astrophysics

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